Problem: Simplify the following expression: $z = \dfrac{9}{5r} + \dfrac{1}{2r}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $5r$ and $2r$ $\lcm(5r, 2r) = 10r$ $ z = \dfrac{2}{2} \cdot \dfrac{9}{5r} + \dfrac{5}{5} \cdot \dfrac{1}{2r} $ $z = \dfrac{18}{10r} + \dfrac{5}{10r}$ $z = \dfrac{18 +5}{10r}$ $z = \dfrac{23}{10r}$